Volterra Kernels Estimation from Noisy Measurements based on the LMS Algorithm or an Errors-In-Variables Method

Zoé Sigrist (1) , Eric Grivel (2) , Benoit Alcoverro

1 Signal/ DESTIN
2 IMS - Laboratoire de l'intégration, du matériau au système

This paper deals with the identification of a nonlinear SISO system modelled by a second-order Volterra series expansion when both the input and the output are disturbed by additive white Gaussian noises. Two methods are proposed. Firstly, we present an unbiased on-line approach based on the LMS. It includes a bias correction scheme which requires the variance of the input additive noise. Secondly, we suggest solving the identification problem as an errors-in-variables issue, by means of the so-called Frisch scheme. Although its computational cost is high, this approach has the advantage of estimating the Volterra kernels and the variances of both the additive noises and the input signal, even if the signal-to-noise ratios at the input and the output are low.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Zoé Sigrist, Eric Grivel, Benoit Alcoverro. Volterra Kernels Estimation from Noisy Measurements based on the LMS Algorithm or an Errors-In-Variables Method. Signal Processing, 2012, 92 (4), pp. 1010-1020. ⟨10.1016/j.sigpro.2011.10.013⟩. ⟨hal-00667284⟩